Flowing liquid

It is also possible to simulate nonequilibrium systems. For example, a bulk liquid can be simulated with periodic boundary conditions that have shifting boundaries. This results in simulating a flowing liquid with laminar flow. This makes it possible to compute properties not measurable in a static fluid, such as the viscosity. Nonequilibrium simulations give rise to additional technical difficulties. Readers of this book are advised to leave nonequilibrium simulations to researchers specializing in this type of work. 

When the liquid target is not a static pool but, rather, a continuous stream of liquid, the added description of dynamic is used. Thus, dynamic FAB and LSIMS refer to bombardment of a continuously renewed (flowing) liquid target. 

In dynamic FAB, this solution is the eluant flowing from an LC column i.e., the target area is covered by a flowing liquid (dynamic) rather than a static one, as is usually the case where FAB is used to examine single substances. The fast atoms or ions from the gun carry considerable momentum, and when they crash into the surface of the liquid some of this momentum is transferred to molecules in the liquid, which splash back out, rather like the result of throwing a stone into a pond (Figure 13.2). This is a very simplistic view of a complex process that also turns the ejected particles into ions (see Chapter 4 for more information on FAB/LSIMS ionization). 

Of the adjustable parameters in the Eyring viscosity equation, kj is the most important. In Sec. 2.4 we discussed the desirability of having some sort of natural rate compared to which rates of shear could be described as large or small. This natural standard is provided by kj. The parameter kj entered our theory as the factor which described the frequency with which molecules passed from one equilibrium position to another in a flowing liquid. At this point we will find it more convenient to talk in terms of the period of this vibration rather than its frequency. We shall use r to symbolize this period and define it as the reciprocal of kj. In addition, we shall refer to this characteristic period as the relaxation time for the polymer. As its name implies, r measures the time over which the system relieves the applied stress by the relative slippage of the molecules past one another. In summary. 

Figure 2.11 (a) The velocity gradient in a flowing liquid, (b) Velocities relative... 

In annular flow, liquid flows as a thin film along the pipe wall and gas flows in the core. Some liquid is entrained as droplets in the gas core. At veiy high gas velocities, nearly all the liquid is entrained as small droplets. Inis pattern is called spray, dispersed, or mist flow. 

Cavitation Loosely regarded as related to water hammer and hydrauhc transients because it may cause similar vibration and equipment damage, cavitation is the phenomenon of collapse of vapor bubbles in flowing liquid. These bubbles may be formed anywhere the local liquid pressure drops below the vapor pressure, or they may be injected into the hquid, as when steam is sparged into water. Local low-pressure zones may be produced by local velocity increases (in accordance with the Bernouhi equation see the preceding Conservation Equations subsection) as in eddies or vortices, or near bound-aiy contours by rapid vibration of a boundaiy by separation of liquid during water hammer or by an overaU reduction in static pressure, as due to pressure drop in the suction line of a pump. 

In the second technique, the flowing liquid must contain scatters in the form of particles or bubbles that will reflect the sound waves. These scatters should be travehng at the velocity of the hquid. A Doppler method is applied by transmitting sound waves along the flow path and measuring the frequency shift in the returned signal from the scatters in the process fluid. This frequency shift is proportional to liquid velocity. 

Viscosity (See Sec. 5 for further information.) In flowing liquids the existence of internal friction or the internal resistance to relative motion of the fluid particles must be considered. This resistance is caUed viscosity. The viscosity of liquids usuaUv decreases with rising temperature. Viscous liquids tend to increase tlie power required by a pump, to reduce pump efficiency, head, and capacity, and to increase Friction in pipe lines. 

For commercial use a partially condensed furan resin is normally prepared which is in the form of a dark free-flowing liquid. Final cure is carried out in situ. 

An incompressible fluid is a fluid whose density remains constant during flow. Liquids are normally treated as being incompressible, as a gas can be when only slight pressure variation occurs. 

Free-flow liquid entry. liquor, forming fine cyclone erode and... 

The second condition is that the well-dispersed slurry forms a homogeneous bed by formation of the bed under well-controlled conditions. This is achieved by a two-step procedure where the bed is formed using constant velocity of the mobile phase and then stabilizing the bed at a constant pressure (Hagel, 1989). The rationale for the first step at constant velocity is that this will create uniform drag forces from the flowing liquid on the gel particles and thus... 

Flow coefficients (not resistance) for valves are generally available from the manufacturer. The coefficient of a valve is defined as tlie flow of water at 60°F, in gallons per minute, at a pressure drop of one pound per square inch across the valve [3], regardless of whether the valve ultimately will be flowing liquid or gases/vapors in the plant process. It is expressed ... 

Reverse flow Liquid flowing from the inlet on one side of the tray (around a center baffle) reverses its direction at the other side of the tray, and flows back to the downcomer on the same side of the tray where the inlet is. 

Split flow Liquid flow across the tray is split into two or more flow paths. 

Mass transfer This phenomenon manifests itself as the physical transport of a metal from one portion of the system to another, and may occur when there is an alloy compositional difference or a temperature gradient between parts of the unit joined by the flowing liquid phase. An exceedingly small solubility of the metal component or corrosion product in the molten metal or salt appears sufficient to permit mass transfer to proceed at a fairly rapid pace. 

Borgstedt and Freeshave shown that for the corrosion of both stabilised and unstabilised austenitic stainless steels in flowing liquid sodium at 700°C there is an almost linear dependence of the corrosion constant, k, on the oxygen content of the sodium, as follows ... 

Gradient across component thickness No. of cycles—high to low No. of cycles—freeze-thaw Solar gain, surface air flow Liquid, moisture, and/or vapor tightness Strength-weight ratios—relative significance Service environment ... 

K. Stulik and V Pacakova, Electroanalytical Measurements in Flowing Liquids, Ellis Horwood, Chichester, 1987. 

Semi-annular flow. Liquid slugs were non-existent (Fig. 2.30e). A liquid film formed at the tube wall with a nearly continuous central vapor core, truncated periodically by churning liquid-vapor zones, which disappear gradually. 

Annular flow (A) existed at high gas superficial velocities and at the entire range of liquid superficial velocities. In annular flow, liquid film formed at the side wall with part of the liquid remaining in the three corners of the channel, while the continuous gas core flowed concurrently with the liquid phase. 

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